{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constructing a NEP polarizability model\n",
    "## Introduction\n",
    "\n",
    "In this tutorial, we will show you how to use the ``GPUMD`` package to train a NEP polarizability model and analyze the results.\n",
    "For theoretical background on the NEP approach, please read the [documentation](https://gpumd.org/potentials/nep). A paper that introduces the NEP polarizability model systematically is in preparation. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prerequisites\n",
    "You need to have access to an NVIDIA GPU with compute capability >= 3.5. Besides it, CUDA Toolkit 9.0 or higher is needed to compile the GPUMD package.\n",
    "The latest GPUMD (we recommend v3.7 or newer) can be downloaded [here](https://github.com/brucefan1983/GPUMD/releases). Unpack it, go to the ``src`` directory, and run the command ``make -j`` to compile. If success, you should get two executables: ``gpumd`` and ``nep`` in the ``src`` directory. The flag \"-std=c++14\" in makefile can be modified to \"-std=c++11\" if you failed the compilation process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train a NEP polarizability model for QM7B database\n",
    "To train a NEP polarizability model, two files: ``train.xyz`` and ``nep.in`` are mandatory. The ``train.xyz`` file contains necessary training data, and the `nep.in` file contains some parameters used for training. Optionally, one can also provide a ``test.xyz`` file that has similar contents as the``train.xyz`` for validation.\n",
    "\n",
    "### Prepare the train.xyz and test.xyz files\n",
    "- The ``train.xyz``/``test.xyz`` file should be prepared according to the [documentation](https://gpumd.org/nep/input_files/).\n",
    "- In this tutorial, ``train.xyz`` and ``test.xyz`` files are already prepared in the current folder, which contain 5768 and 1443 structures, respectively. Structures as well as polarizability data in the ``train.xyz`` and ``test.xyz`` are taken from the [QM7B database](https://archive.materialscloud.org/record/2019.0002/v2) that contains 7211 organic compounds. The (static) polarizability is a symmetric second-order tensor that has a form of \n",
    "$$\\boldsymbol{\\alpha }=\\left( \\begin{matrix}\n",
    "\t\\alpha _{xx}&\t\t\\alpha _{xy}&\t\t\\alpha _{xz}\\\\\n",
    "\t\\alpha _{yx}&\t\t\\alpha _{yy}&\t\t\\alpha _{yz}\\\\\n",
    "\t\\alpha _{zx}&\t\t\\alpha _{zy}&\t\t\\alpha _{zz}\\\\\n",
    "\\end{matrix} \\right) $$\n",
    "The polarizability data are embedded in the comment lines of ``train.xyz``/``test.xyz``, organized as *pol=\"\t$\\alpha _{xx}$  $\\alpha _{xy} $  $\\alpha _{xz}$\t$\\alpha _{yx}$  $\\alpha _{yy} $  $\\alpha _{yz}$ \t$\\alpha _{zx}$  $\\alpha _{zy} $  $\\alpha _{zz}$\"* per structure. The polarizability data were computed at the CCSD/d-aug-cc-pVDZ level of theory by [Yang and collaborators](https://www.nature.com/articles/s41597-019-0157-8). Of course, you can use any quantum mechanics package and any theoretical method such as the DFT to calculate the polarizability. However, structures in [QM7B database](https://archive.materialscloud.org/record/2019.0002/v2) are without lattice information, which is mandatory in the training of NEP models. Therefore, a cubic box with a dimension of 100 $\\rm \\mathring{A}$ was set for every structure. We recommend the [ASE package](https://wiki.fysik.dtu.dk/ase/) to manipulate the ``train.xyz``/``test.xyz`` file.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the `nep.in` file. \n",
    "- First, read the [documentation](https://gpumd.org/nep/input_files/) regarding input paramaters carefully. The most important parameter is `model_type`, which controls the training types. `model_type=0` which is default, stands for a training task of PES;`model_type=1`, a training task of dipole; `model_type=2`, a training task of polarizability. Here, we set `model_type=2`.     \n",
    "A minimal ``nep.in`` file reads:\n",
    "```\n",
    "type        6 H C N O S Cl\t\n",
    "model_type        2\n",
    "```\n",
    "The parameter `type` is also important, which specified the element kinds in the system. The first value `6` is the number of elements in ``train.xyz``/``test.xyz``, followed by the detailed element names, in this case, `H C N O S Cl`. **The order will be frozen in the model after training.** We have prepared the ``nep.in`` file in the current folder, which reads:\n",
    "```\n",
    "type         6 H C N O S Cl\t\n",
    "model_type         2\n",
    "cutoff       6 4\n",
    "n_max        6 6\n",
    "basis_size    10 10\n",
    "l_max        4 2 1\n",
    "neuron       10\n",
    "population    80\n",
    "batch        10000\n",
    "generation   200000\n",
    "lambda_1     0.03\n",
    "lambda_2     0.03\n",
    "```\n",
    "\n",
    "The values of parameters `cutoff`, `n_max`,`basis_size`,`l_max`, `neuron`,`population` used here were tested elaborately, which achieved a good balance between the accuracy and costs. The batch size depends on your GPU device. On a GeForce RTX 3090 with 24 GB memory, you can train the model with all data at the same time, therefore, we set `batch ` a value greater than 5768. The `lambda_1` and `lambda_1` are the [regularization paramaters](https://gpumd.org/nep/input_parameters/lambda_1.html). You can **take the default values trustingly just ignore these two parameters.** The `GPUMD` will adjust these two parameters dynamically according to the real-time loss. Alternatively, you can set  lambda_1 and lambda_2 a fixed value which should be of the [same order as the target quantities]((https://gpumd.org/nep/input_parameters/lambda_1.html)) upon convergence. In this example, we set `lambda_1=lambda_2=0.03`.We will look back on it after analyzing the results.\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run the ``nep`` executable\n",
    " - Run the following command in the working directory\n",
    "```\n",
    "path/to/nep # if you use linux\n",
    "path\\to\\nep # if you use Windows\n",
    "```\n",
    " \n",
    "It took about 22 hours to run 200,000 generations using a GeForce RTX 3090. One can kill the task at any time and also restart it just by running the `nep` again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check the training results\n",
    "\n",
    "- After you launch the `nep` task, there should be some output on the screen. We encourage the user to read the screen output carefully. It can help to understand the working flow of `nep`. \n",
    "- Some files will be generated in the current folder and will be updated every 100 generations (some will be updated every 1000 generations). Therefore, one can check the results even before finishing the maximum number of generations as set in `nep.in`. \n",
    "- If the user has not read the documentation regarding the output files, it is time to read about those [here](https://gpumd.org/nep/output_files/).\n",
    "- We will use Python to visualize the results in some of the output files next. We first load ``pylab`` that we need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking the ``loss.out`` file\n",
    "- We see that the $\\mathcal{L}_1$ and $\\mathcal{L}_2$ regularization loss functions first increases and then decreases, which indicates the effectiveness of the regularization.\n",
    "- The polarizability loss is the root mean square error (RMSE) of polarizability per atom, which converges to about 0.03-0.04 a.u./atom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss = loadtxt('loss.out')\n",
    "loglog(loss[:, 1:4])\n",
    "loglog(loss[:, 4:6])\n",
    "xlabel('Generation/100')\n",
    "ylabel('Loss')\n",
    "legend(['Total', 'L1-regularization', 'L2-regularization', 'Polarizability-train', 'Polarizability-train'])\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The loss terms 'Polarizability-train' and 'Polarizability-train' converged after 20,000 generations (But you can run it longer). That's why we choose the paramaters `lambda_1=lambda_2=0.03`. But you can **take the default values trustingly**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking the `polarizability_test.out` file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `polarizability_test.out` is organized as \"$\\alpha _{xx}$  $\\alpha _{yy} $  $\\alpha _{zz}$\t $\\alpha _{xy}$  $\\alpha _{yz} $  $\\alpha _{xz}$ $\\alpha _{xx}$  $\\alpha _{yy} $  $\\alpha _{zz}$\t $\\alpha _{xy}$  $\\alpha _{yz} $  $\\alpha _{xz}$\", one line per structure. The first six values are predicted by `NEP`, while the last six values are the references we provide in `test.xyz`(but divided by the number of atoms)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for diagonal elements\n",
    "pol_diag_test = loadtxt('polarizability_test.out',usecols=(0,1,2,6,7,8))\n",
    "ref_values = np.hstack([pol_diag_test[:,3],pol_diag_test[:,4],pol_diag_test[:,5]])\n",
    "nep_values = np.hstack([pol_diag_test[:,0],pol_diag_test[:,1],pol_diag_test[:,2]])\n",
    "plot(ref_values,nep_values , '.')\n",
    "plot(linspace(pol_diag_test.min(),pol_diag_test.max()), linspace(pol_diag_test.min(),pol_diag_test.max()), '-')\n",
    "xlim((pol_diag_test.min(),pol_diag_test.max()))\n",
    "ylim((pol_diag_test.min(),pol_diag_test.max()))\n",
    "xlabel('Reference diagonal polarizability (a.u./atom)')\n",
    "ylabel('NEP diagonal polarizability (a.u./atom)')\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(4,4)\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for off-diagonal elements\n",
    "pol_offdiag_test = loadtxt('polarizability_test.out',usecols=(3,4,5,9,10,11))\n",
    "ref_values = np.hstack([pol_offdiag_test[:,3],pol_offdiag_test[:,4],pol_offdiag_test[:,5]])\n",
    "nep_values = np.hstack([pol_offdiag_test[:,0],pol_offdiag_test[:,1],pol_offdiag_test[:,2]])\n",
    "plot(ref_values,nep_values , '.')\n",
    "plot(linspace(pol_offdiag_test.min(),pol_offdiag_test.max()), linspace(pol_offdiag_test.min(),pol_offdiag_test.max()), '-')\n",
    "xlim((pol_offdiag_test.min(),pol_offdiag_test.max()))\n",
    "ylim((pol_offdiag_test.min(),pol_offdiag_test.max()))\n",
    "xlabel('Reference off-diagonal polarizability (a.u./atom)')\n",
    "ylabel('NEP off-diagonal polarizability (a.u./atom)')\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(4,4)\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get molecular polarizability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numbers of atoms are varied for different structures in the QM7B database. To get their polarizability, we should know their numbers of atoms. The following `Python` script can be used to obtain the molecular polarizability for each structure in `test.xyz`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diagonal elements:\n",
      "[[ 86.93239  81.89478  64.59779  86.77072  81.95972  63.94601]\n",
      " [ 66.87154  75.06843  70.12993  67.42251  75.463    70.00906]\n",
      " [ 95.30625  72.51928  69.21652  95.10905  72.87611  68.8432 ]\n",
      " ...\n",
      " [ 65.3233   67.70946  55.286    65.57978  67.49064  55.38372]\n",
      " [ 78.4861  118.855    47.02907  77.48224 119.3984   47.36193]\n",
      " [ 68.6895   70.45695  68.69175  68.29755  70.4676   68.9577 ]]\n",
      "Off-diagonal elements:\n",
      "[[-2.1363730e+00 -2.0750540e+00  7.9340360e+00 -1.8626050e+00\n",
      "  -1.8792140e+00  7.2918270e+00]\n",
      " [ 1.8631660e+00  1.6867077e+00  8.0070000e-01  2.1008430e+00\n",
      "   1.8908760e+00  6.6708000e-01]\n",
      " [ 1.4109745e+01  3.6405840e+00  1.7375190e+00  1.4100157e+01\n",
      "   3.8441590e+00  1.6899003e+00]\n",
      " ...\n",
      " [ 6.9831720e-01 -1.1632208e+00  6.2205360e+00  9.8580300e-01\n",
      "  -9.8249060e-01  6.4980860e+00]\n",
      " [ 3.3778140e+01 -6.1842220e-02  2.8229300e-02  3.3851840e+01\n",
      "  -8.4909000e-02  2.3642960e-02]\n",
      " [-1.2690855e-01  9.5440650e-02 -8.6488950e+00 -1.1436195e-01\n",
      "   9.4393050e-02 -8.2682400e+00]]\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "file_size = os.path.getsize(\"test.xyz\")\n",
    "noa_list = []\n",
    "with open(\"test.xyz\") as reader:\n",
    "    while (reader.tell() < file_size):\n",
    "        noa = int(reader.readline())\n",
    "        noa_list.append(noa)\n",
    "        for i in range(noa+1):\n",
    "            reader.readline()\n",
    "\n",
    "atomic_pol_diag_test = loadtxt('polarizability_test.out',usecols=(0,1,2,6,7,8))\n",
    "            \n",
    "molecular_diagonal_polarizability = atomic_pol_diag_test * np.tile(np.array(noa_list).reshape(-1,1),(1,6))\n",
    "print(\"Diagonal elements:\")\n",
    "print(molecular_diagonal_polarizability)\n",
    "\n",
    "atomic_pol_offdiag_test = loadtxt('polarizability_test.out',usecols=(3,4,5,9,10,11))\n",
    "            \n",
    "molecular_offdiag_polarizability = atomic_pol_offdiag_test * np.tile(np.array(noa_list).reshape(-1,1),(1,6))\n",
    "print(\"Off-diagonal elements:\")\n",
    "print(molecular_offdiag_polarizability)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction\n",
    "- You can switch the workding mode from training to prediction by adding an extra parameter `prediction 1` in `nep.in`, and provide a `train.xyz`. In this mode, the polarizability data is not necessary in `train.xyz`. The `NEP` will use `-1e+06` as the reference values in `polarizability_train.out`. We also provide an example in the `prediction_new_molecule` directory.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Restart\n",
    "- After each 100 steps, the ``nep.restart`` file will be updated.\n",
    "- If ``nep.restart`` exists, it means you want to continue the previous training. Remember not to change the parameters related to the descriptor and the number of neurons. Otherwise the restarting behavior is undefined.\n",
    "- If you want to train from scratch, you need to delete ``nep.restart`` first (better to first make a copy of all the results from the previous training)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Author "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nan Xu \n",
    "\n",
    "tamas@zju.edu.cn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
